Acceleration of charged particles by wake waves excited by an electron bunch in a collisional plasma

One of the promising possibilities for accelerating charged particles to high energies (approx-gt 1 GeV) at high rates (approx-gt 100 MeV/m) is to use the wake plasma wave excited in a plasma by a single electron bunch or a sequence of bunches. Efficient acceleration to energies greater than the energy of electrons in the bunch is possible if the accelerating particles are acted on by a field with amplitude E+ considerably greater than that of the field E- in which the electrons in the bunch are slowed down. So far, is has been proposed that wake acceleration be done using single bunches with a strictly defined temporal density profile that is close to triangular, sequences of bunches with precisely selected pulse durations and pauses between them, nonlinear plasma oscillations excited by bunches with a density close to the plasma density close to the plasma density, and spatially distributed beams of accelerated particle and particles that have been excited by an accelerating field. In this paper the authors examine analytically and in a one-dimensional approximation the possibility of collectively accelerating electrons by the wake plasma wave excited in a collisional plasma by a single electron bunch